Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non‐normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project.
Mixture regression models have been widely used in business, marketing and social sciences to model mixed regression relationships arising from a clustered and thus heterogeneous population. The unknown mixture regression parameters are usually estimated by maximum likelihood estimators using the expectation–maximisation algorithm based on the normality assumption of component error density. However, it is well known that the normality‐based maximum likelihood estimation is very sensitive to outliers or heavy‐tailed error distributions. This paper aims to give a selective overview of the recently proposed robust mixture regression methods and compare their performance using simulation studies.
more » « less- NSF-PAR ID:
- 10457879
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- International Statistical Review
- Volume:
- 88
- Issue:
- 1
- ISSN:
- 0306-7734
- Page Range / eLocation ID:
- p. 176-202
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Discussion The results suggested that the allometric relationships between body mass and different skeletal traits are largely conserved among populations. The revised method provided improved applicability with strong underlying theoretical justifications, and potential for future improvements.
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